Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$

Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^*%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Makarychev, Sergei [verfasserIn] Vyugin, Ilya

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Polynomial Algebraic equation Field of positive characteristic Subgroup

Anmerkung:	© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019

Übergeordnetes Werk:	Enthalten in: Arnold mathematical journal - Berlin [u.a.] : Springer, 2015, 5(2019), 1 vom: März, Seite 105-121
Übergeordnetes Werk:	volume:5 ; year:2019 ; number:1 ; month:03 ; pages:105-121

Links:	Volltext

DOI / URN:	10.1007/s40598-019-00112-z

Katalog-ID:	SPR036741108

Internformat


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520			\|a Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^*%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy.
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700	1		\|a Vyugin, Ilya \|0 (orcid)0000-0002-7430-9006 \|4 aut
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912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
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912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
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912			\|a GBV_ILN_4336
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952			\|d 5 \|j 2019 \|e 1 \|c 03 \|h 105-121

Indexfelder

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matchkey_str	article:21996806:2019----::ouinoplnmaeutosnugo
hierarchy_sort_str	2019
publishDate	2019
allfields	10.1007/s40598-019-00112-z doi (DE-627)SPR036741108 (SPR)s40598-019-00112-z-e DE-627 ger DE-627 rakwb eng Makarychev, Sergei verfasserin aut Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019 Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213 Vyugin, Ilya (orcid)0000-0002-7430-9006 aut Enthalten in Arnold mathematical journal Berlin [u.a.] : Springer, 2015 5(2019), 1 vom: März, Seite 105-121 (DE-627)815913737 (DE-600)2806570-0 2199-6806 nnns volume:5 year:2019 number:1 month:03 pages:105-121 https://dx.doi.org/10.1007/s40598-019-00112-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 5 2019 1 03 105-121
spelling	10.1007/s40598-019-00112-z doi (DE-627)SPR036741108 (SPR)s40598-019-00112-z-e DE-627 ger DE-627 rakwb eng Makarychev, Sergei verfasserin aut Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019 Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213 Vyugin, Ilya (orcid)0000-0002-7430-9006 aut Enthalten in Arnold mathematical journal Berlin [u.a.] : Springer, 2015 5(2019), 1 vom: März, Seite 105-121 (DE-627)815913737 (DE-600)2806570-0 2199-6806 nnns volume:5 year:2019 number:1 month:03 pages:105-121 https://dx.doi.org/10.1007/s40598-019-00112-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 5 2019 1 03 105-121
allfields_unstemmed	10.1007/s40598-019-00112-z doi (DE-627)SPR036741108 (SPR)s40598-019-00112-z-e DE-627 ger DE-627 rakwb eng Makarychev, Sergei verfasserin aut Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019 Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213 Vyugin, Ilya (orcid)0000-0002-7430-9006 aut Enthalten in Arnold mathematical journal Berlin [u.a.] : Springer, 2015 5(2019), 1 vom: März, Seite 105-121 (DE-627)815913737 (DE-600)2806570-0 2199-6806 nnns volume:5 year:2019 number:1 month:03 pages:105-121 https://dx.doi.org/10.1007/s40598-019-00112-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 5 2019 1 03 105-121
allfieldsGer	10.1007/s40598-019-00112-z doi (DE-627)SPR036741108 (SPR)s40598-019-00112-z-e DE-627 ger DE-627 rakwb eng Makarychev, Sergei verfasserin aut Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019 Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213 Vyugin, Ilya (orcid)0000-0002-7430-9006 aut Enthalten in Arnold mathematical journal Berlin [u.a.] : Springer, 2015 5(2019), 1 vom: März, Seite 105-121 (DE-627)815913737 (DE-600)2806570-0 2199-6806 nnns volume:5 year:2019 number:1 month:03 pages:105-121 https://dx.doi.org/10.1007/s40598-019-00112-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 5 2019 1 03 105-121
allfieldsSound	10.1007/s40598-019-00112-z doi (DE-627)SPR036741108 (SPR)s40598-019-00112-z-e DE-627 ger DE-627 rakwb eng Makarychev, Sergei verfasserin aut Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^%$ 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019 Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213 Vyugin, Ilya (orcid)0000-0002-7430-9006 aut Enthalten in Arnold mathematical journal Berlin [u.a.] : Springer, 2015 5(2019), 1 vom: März, Seite 105-121 (DE-627)815913737 (DE-600)2806570-0 2199-6806 nnns volume:5 year:2019 number:1 month:03 pages:105-121 https://dx.doi.org/10.1007/s40598-019-00112-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 5 2019 1 03 105-121
language	English
source	Enthalten in Arnold mathematical journal 5(2019), 1 vom: März, Seite 105-121 volume:5 year:2019 number:1 month:03 pages:105-121
sourceStr	Enthalten in Arnold mathematical journal 5(2019), 1 vom: März, Seite 105-121 volume:5 year:2019 number:1 month:03 pages:105-121
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Polynomial Algebraic equation Field of positive characteristic Subgroup
isfreeaccess_bool	false
container_title	Arnold mathematical journal
authorswithroles_txt_mv	Makarychev, Sergei @@aut@@ Vyugin, Ilya @@aut@@
publishDateDaySort_date	2019-03-01T00:00:00Z
hierarchy_top_id	815913737
id	SPR036741108
language_de	englisch
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author	Makarychev, Sergei
spellingShingle	Makarychev, Sergei misc Polynomial misc Algebraic equation misc Field of positive characteristic misc Subgroup Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$
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topic_title	Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$ Polynomial (dpeaa)DE-He213 Algebraic equation (dpeaa)DE-He213 Field of positive characteristic (dpeaa)DE-He213 Subgroup (dpeaa)DE-He213
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title	Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$
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title_full	Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$
author_sort	Makarychev, Sergei
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author_browse	Makarychev, Sergei Vyugin, Ilya
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author-letter	Makarychev, Sergei
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title_sort	solutions of polynomial equations in subgroups of %$\mathbb {f}_p^*%$
title_auth	Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$
abstract	Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^*%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019
abstractGer	Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^*%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019
abstract_unstemmed	Abstract We present an upper bound on the number of solutions of an algebraic equation %$P(x,y)=0%$ where x and y belong to the union of cosets of some subgroup of the multiplicative group %$\kappa ^*%$ of some field of positive characteristic. This bound generalizes the bound of Corvaja and Zannier (J Eur Math Soc 15(5):1927–1942, 2013) to the case of union of cosets. We also obtain the upper bounds on the generalization of additive energy. © Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019
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title_short	Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$
url	https://dx.doi.org/10.1007/s40598-019-00112-z
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up_date	2024-07-03T19:23:21.854Z
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Solutions of Polynomial Equations in Subgroups of %$\mathbb {F}_p^*%$

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